Monotonicity of stable solutions in shadow systems

A shadow system appears as a limit of a reaction-diffusion system in which some components have infinite diffusivity. We investigate the spatial structure of its stable solutions. It is known that, unlike scalar reaction-diffusion equations, some shadow systems may have stable nonconstant (monotone) solutions. On the other hand, it is also known that in autonomous shadow systems any nonconstant non-monotone stationary solution is necessarily unstable. In this paper, it is shown in a general setting that any stable bounded (not necessarily stationary) solution is asymptotically homogeneous or eventually monotone in .

     

Irradiation-Dependent Saturable Absorption Properties in Dye-Doped Polyvinyl Alcohol Films Exposed to a Highly Humid Atmosphere

Effects of humidity on nonlinear transmission properties due to saturable absorption were investigated using eosin-Y-doped polyvinyl alcohol (PVA) films which had been exposed to a highly humid atmosphere. In a pump-probe measurement, a transmitted probe signal changed in every shot of the pump-pulse irradiation, and tended to approach a steady characteristic. Simultaneous measurements of the transmitted probe power and the phosphorescent lifetime showed that these phenomena stem from the phosphorescent lifetime being lengthened by the successive pump irradiations. This increase in lifetime was found to have originated from reduction of a nonradiative decay rate of an excited state of the dyes. The recurrent pump irradiations are believed to remove moisture, which has strengthened the nonradiative decay rate, from the PVA films.     

Quantitative assessment of the degree of hoarseness

By using a computer simulation, the author examined the theoretically expected discrepancy of the obtained H/N ratio from the real H/N value, the effects of perturbatios of pitch, and amplitude on the H/N ratio and others. Regarding the averaged wave as an estimate of the harmonic component, resulted in harmonic energy greater than its real value. The H/N ratio method detected perturbations of pitch and amplitude as a quantity of noise energy. The effect of pitch perturbation on the H/N ratio was much greater than that of amplitude perturbation. The error range of the measurement system did not contribute significantly to the calculated H/N ratios.     

Singular surfaces in a linear thermo-elastic dielectric material

Singular surfaces in a linear thermo-elastic dielectric material are considered, where the constitutive equations of the elastic dielectric proposed by Toupin and the heat equations with finite wave velocities are combined. There exist six types of singular surfaces including a stationary one. The velocities, the coupled fields and the variation of the amplitudes of the surfaces with respect to time are investigated. It is found that the amplitude of the mechanical transverse wave rotates during propagation and at the stationary surface the amplitude of the electric field periodically reverses in direction and the one of the polarization field rotates elliptically with the same period.     

Enantio- and diastereomerically pure threo-homoallylic alcohols via highly stereoselective reduction of α-methyl-β,γ-unsaturated ketones

Reduction of α-methyl-β,γ-unsaturated ketones with L-Selectride proceeded with high $\text{threo}$-selectivity to afford $\text{threo}$-β-methyl homoallylic alcohols of high enantio- and diastereomerical purities.